\(2\log{(a -2b)} = \log{a} + \log{b}\)
We can write
log ( a - 2b)^2 = log (ab)
We have the logs the same......we can solve this
(a - 2b)^2 = ab
a^2 - 4ab + 4b^2 = ab
a^2 - 5ab + 4b^2 = 0 factor as
(a - 4b) ( a - b) = 0
So either
a - 4b = 0 or a - b = 0
a = 4b a = b
a/b = 4 a/b = 1